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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 25659, 816]*) (*NotebookOutlinePosition[ 26357, 840]*) (* CellTagsIndexPosition[ 26313, 836]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ \(<< xlr8r.m\)], "Input", CellLabel->"In[62]:="], Cell[BoxData[ \("xlr8r 0.21 (13-August-2005) loaded 20-August-2005 21:11:42.547120 \ using Mathematica 5.2 for Mac OS X (June 20, 2005)"\)], "Print", CellLabel->"From In[62]:="] }, Open ]], Cell["\<\ Auxin/Pin1 Pathway calculation BES 13 Aug 2005 Based on email notes EMJ 13 Aug 2005 Appendix I added by EMj 20 Aug 2005 EMj on the date: all dates above should actually be 20 Aug - 13 Aug was \ *last* Saturday.\ \>", "Text"], Cell[CellGroupData[{ Cell[TextData[{ "Reaction 1: ", Cell[BoxData[ \({B\_\(j, m - 1\) \[RightArrowLeftArrow] \ B\_\(j, m\), \ A\_j[t] \((n - m + 1)\) k\_f, \ m*k\_r}\)]] }], "SectionFirst"], Cell[BoxData[ \(step[m_, n_] := {B\_\(j, m - 1\) \[RightArrowLeftArrow] \ B\_\(j, m\), \ A\_j[t] \((n - m + 1)\) k\_f, \ m*k\_r}\)], "Input", CellLabel->"In[63]:="], Cell[CellGroupData[{ Cell[BoxData[ \(net = Table[step[m, 4], \ {m, 1, 4}]\)], "Input", CellLabel->"In[64]:="], Cell[BoxData[ \({{B\_\(j, 0\) \[RightArrowLeftArrow] B\_\(j, 1\), 4\ k\_f\ A\_j[t], k\_r}, {B\_\(j, 1\) \[RightArrowLeftArrow] B\_\(j, 2\), 3\ k\_f\ A\_j[t], 2\ k\_r}, {B\_\(j, 2\) \[RightArrowLeftArrow] B\_\(j, 3\), 2\ k\_f\ A\_j[t], 3\ k\_r}, {B\_\(j, 3\) \[RightArrowLeftArrow] B\_\(j, 4\), k\_f\ A\_j[t], 4\ k\_r}}\)], "Output", CellLabel->"Out[64]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(interpret[net]\)[\([1]\)]\)], "Input", CellLabel->"In[65]:="], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox[\(B\_\(j, 0\)\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", \(\(-4\)\ k\_f\ A\_j[t]\ B\_\(j, 0\)[t] + k\_r\ B\_\(j, 1\)[t]\)}], ",", RowBox[{ RowBox[{ SuperscriptBox[\(B\_\(j, 1\)\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", \(4\ k\_f\ A\_j[t]\ B\_\(j, 0\)[t] - k\_r\ B\_\(j, 1\)[t] - 3\ k\_f\ A\_j[t]\ B\_\(j, 1\)[t] + 2\ k\_r\ B\_\(j, 2\)[t]\)}], ",", RowBox[{ RowBox[{ SuperscriptBox[\(B\_\(j, 2\)\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", \(3\ k\_f\ A\_j[t]\ B\_\(j, 1\)[t] - 2\ k\_r\ B\_\(j, 2\)[t] - 2\ k\_f\ A\_j[t]\ B\_\(j, 2\)[t] + 3\ k\_r\ B\_\(j, 3\)[t]\)}], ",", RowBox[{ RowBox[{ SuperscriptBox[\(B\_\(j, 3\)\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", \(2\ k\_f\ A\_j[t]\ B\_\(j, 2\)[t] - 3\ k\_r\ B\_\(j, 3\)[t] - k\_f\ A\_j[t]\ B\_\(j, 3\)[t] + 4\ k\_r\ B\_\(j, 4\)[t]\)}], ",", RowBox[{ RowBox[{ SuperscriptBox[\(B\_\(j, 4\)\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "\[Equal]", \(k\_f\ A\_j[t]\ B\_\(j, 3\)[t] - 4\ k\_r\ B\_\(j, 4\)[t]\)}]}], "}"}]], "Output", CellLabel->"Out[65]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[{0 \[Equal] \(-4\)\ k\_f\ A\_j[t]\ B\_\(j, 0\)[t] + k\_r\ B\_\(j, 1\)[t], 0 \[Equal] 4\ k\_f\ A\_j[t]\ B\_\(j, 0\)[t] - k\_r\ B\_\(j, 1\)[t] - 3\ k\_f\ A\_j[t]\ B\_\(j, 1\)[t] + 2\ k\_r\ B\_\(j, 2\)[t], 0 \[Equal] 3\ k\_f\ A\_j[t]\ B\_\(j, 1\)[t] - 2\ k\_r\ B\_\(j, 2\)[t] - 2\ k\_f\ A\_j[t]\ B\_\(j, 2\)[t] + 3\ k\_r\ B\_\(j, 3\)[t], 0 \[Equal] 2\ k\_f\ A\_j[t]\ B\_\(j, 2\)[t] - 3\ k\_r\ B\_\(j, 3\)[t] - k\_f\ A\_j[t]\ B\_\(j, 3\)[t] + 4\ k\_r\ B\_\(j, 4\)[t], 0 \[Equal] k\_f\ A\_j[t]\ B\_\(j, 3\)[t] - 4\ k\_r\ B\_\(j, 4\)[t], \[IndentingNewLine]BT \[Equal] B\_\(j, 0\)[t] + B\_\(j, 1\)[t] + B\_\(j, 2\)[t] + B\_\(j, 3\)[t] + B\_\(j, 4\)[t]}, \[IndentingNewLine]{B\_\(j, 0\)[t], B\_\(j, 1\)[t], B\_\(j, 2\)[t], B\_\(j, 3\)[t], B\_\(j, 4\)[t]}]\)], "Input", CellLabel->"In[66]:="], Cell[BoxData[ \({{B\_\(j, 0\)[ t] \[Rule] \(BT\ k\_r\%4\)\/\((k\_r + k\_f\ A\_j[t])\)\^4, B\_\(j, 1\)[ t] \[Rule] \(4\ BT\ k\_f\ k\_r\%3\ A\_j[t]\)\/\((k\_r + k\_f\ \ A\_j[t])\)\^4, B\_\(j, 2\)[ t] \[Rule] \(6\ BT\ k\_f\%2\ k\_r\%2\ A\_j[t]\^2\)\/\((k\_r + \ k\_f\ A\_j[t])\)\^4, B\_\(j, 3\)[ t] \[Rule] \(4\ BT\ k\_f\%3\ k\_r\ A\_j[t]\^3\)\/\((k\_r + k\_f\ \ A\_j[t])\)\^4, B\_\(j, 4\)[ t] \[Rule] \(BT\ k\_f\%4\ A\_j[t]\^4\)\/\((k\_r + k\_f\ \ A\_j[t])\)\^4}}\)], "Output", CellLabel->"Out[66]="] }, Open ]], Cell[TextData[{ "steady state solution :", Cell[BoxData[ \(B\_\(j, 4\)[ t] \[Rule] \(BT\ k\_f\%4\ A\_j[t]\^4\)\/\((k\_r + k\_f\ \ A\_j[t])\)\^4\)], FontSize->24], "\[TildeTilde]", Cell[BoxData[ \(\(BT\ k\_f\%4\ A\_j[t]\^4\)\/\((k\_r)\)\^4\)], FontSize->24], " in the approx. 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